Question: Express your answer as a mixed number simplified to lowest terms. $8\dfrac{1}{3}-5\dfrac{6}{17} = {?}$
Find a common denominator for the fractions: $= {8\dfrac{17}{51}}-{5\dfrac{18}{51}}$ Convert ${8\dfrac{17}{51}}$ to ${7 + \dfrac{51}{51} + \dfrac{17}{51}}$ So the problem becomes: ${7\dfrac{68}{51}}-{5\dfrac{18}{51}}$ Separate the whole numbers from the fractional parts: $= {7} + {\dfrac{68}{51}} - {5} - {\dfrac{18}{51}}$ Bring the whole numbers together and the fractions together: $= {7} - {5} + {\dfrac{68}{51}} - {\dfrac{18}{51}}$ Subtract the whole numbers: $=2 + {\dfrac{68}{51}} - {\dfrac{18}{51}}$ Subtract the fractions: $= 2+\dfrac{50}{51}$ Combine the whole and fractional parts into a mixed number: $= 2\dfrac{50}{51}$